Firstly what is TUC-R. I wasn't aware TUC had been remastered.Onscreen starbases were located on planets
There was only one starbase (definitively) shown onscreen in pre-remastered TOS, AFAIK: Starbase 11. But that doesn't mean the "space station" isn't part or all of a starbase. The flower badge might be evidence that it is.
The "space station" in TUC-R is Starbase 6.
And TOS-R is retconning. TOS-R changed the station design in "The Ultimate Computer" for the sake of change despite the fact that it's still referred to as a station rather than a base or starbase. So like the "new" Defiant emblem seen IAMD it's a retcon that has no weight in terms to what TOS was trying to depict originally.
By TUC-R, I meant "The Ultimate Computer," remastered. Only one sentence in my post discusses TOS-R. The rest applies to TOS pre-remastered, as I said.
So, again, how many starbases were definitively shown in pre-remastered TOS? Enough to conclude that the space station in "The Ultimate Computer" was not some or all of a starbase?